Oct 4, 2018 11:29 PM
http://chalkdustmagazine.com/front-page-...f-nothing/
EXCERPT: . . . The main point is: How to deal with zero. You can start with nothing and say: something is the opposite of zero. On the other hand, one can say: zero is already something, I can count it: one element. But first things first. I would like to start with an old fear of people: the fear of emptiness. The Romans had no zero. For centuries physicists were afraid of the so-called horror vacui based on the idea of Aristotle that nature could not create any emptiness at all (Aristotle). Even in art, there is the horror vacui as criticism of the art of the Victorian era (Mario Praz, 6/09/1986-23/03/1982).
Let us take one step back and start with sets. Why sets? Before we can handle this let us ask something else: How can a science be justified? Religions work with dogmas. You need one example? Here it is: God is good and almighty. There is no further proof of this, for it has been established as a statement. Mathematics does not work with dogmas. You can start with something else: axioms.
What is an axiom? The word axiom comes from the Greek and means “perceived principle” and is in a theory, a science or an axiomatic system something that is not founded or deductively derived within this system. One amazing hint: Insufficiently strong systems, such as arithmetic, there must be statements that can neither be formally proven nor refuted (this is called the Gödel incompleteness theorem).
For a long time, mathematicians tried to design a clean axiomatic system. After many trials and errors, they decided to try it with quantities. So-called sets and finally we are in set theory. Set theory is a fundamental branch of mathematics that deals with the investigation of sets, i.e. summaries of objects. Set theory was founded by Georg Cantor and deals with representing (mathematical) objects as sets. By a set, we mean every summary M of certain well-different objects in our intuition or thinking (which are called the elements of M) into a whole. You need some examples...
MORE: http://chalkdustmagazine.com/front-page-...f-nothing/
EXCERPT: . . . The main point is: How to deal with zero. You can start with nothing and say: something is the opposite of zero. On the other hand, one can say: zero is already something, I can count it: one element. But first things first. I would like to start with an old fear of people: the fear of emptiness. The Romans had no zero. For centuries physicists were afraid of the so-called horror vacui based on the idea of Aristotle that nature could not create any emptiness at all (Aristotle). Even in art, there is the horror vacui as criticism of the art of the Victorian era (Mario Praz, 6/09/1986-23/03/1982).
Let us take one step back and start with sets. Why sets? Before we can handle this let us ask something else: How can a science be justified? Religions work with dogmas. You need one example? Here it is: God is good and almighty. There is no further proof of this, for it has been established as a statement. Mathematics does not work with dogmas. You can start with something else: axioms.
What is an axiom? The word axiom comes from the Greek and means “perceived principle” and is in a theory, a science or an axiomatic system something that is not founded or deductively derived within this system. One amazing hint: Insufficiently strong systems, such as arithmetic, there must be statements that can neither be formally proven nor refuted (this is called the Gödel incompleteness theorem).
For a long time, mathematicians tried to design a clean axiomatic system. After many trials and errors, they decided to try it with quantities. So-called sets and finally we are in set theory. Set theory is a fundamental branch of mathematics that deals with the investigation of sets, i.e. summaries of objects. Set theory was founded by Georg Cantor and deals with representing (mathematical) objects as sets. By a set, we mean every summary M of certain well-different objects in our intuition or thinking (which are called the elements of M) into a whole. You need some examples...
MORE: http://chalkdustmagazine.com/front-page-...f-nothing/